A098507 Diagonal sums of the number triangle A098505.

1, 1, 2, 2, 5, 6, 10, 9, 19, 22, 65, 88, 114, 187, 395, 376, 888, 520, 2645, 2017, 3303, 3590, 8820, 9408, 5785, 7792, 24181, 27047, 74720, 68731, 153394, 159394, 369957, 1261522, 4326030, 4924898, 6538595, 9754155, 10068484, 10541264, 24936678

Offset

0,3

Links

Table of n, a(n) for n=0..40.

Formula

a(n) = Sum_{k=0..floor(n/2)} numerator((n-k+1)*binomial(n-k, k)/binomial(2*n-2*k, n-k)).

Mathematica

Table[Sum[Numerator[(n-k+1) Binomial[n-k, k]/Binomial[2n-2k, n-k]], {k, 0, Floor[ n/2]}], {n, 0, 60}] (* Harvey P. Dale, Jun 19 2021 *)

Crossrefs

Cf. A098505.

Sequence in context: A348757 A118807 A240309 * A097066 A035548 A240059

Adjacent sequences: A098504 A098505 A098506 * A098508 A098509 A098510

Keyword

easy,nonn

Author

Paul Barry, Sep 11 2004

Status

approved